CN1818952A - Resource object planning optimizing distribution of combined operation information war - Google Patents

Abstract

A information war resource aim programming most superior assign method of combined operations, belongs to the military and the correlative field, the object of the most superior assignment is the information war resource of the combined operations, the method is: define the property of the information war resource assignment and the information war battle effectiveness, construct the assignment rules of the information war resource, setup the model of the most superior assignment of the information war resource according to the battle effectiveness needing guideline of the information war resource, use the aim programming method to find the module, finally get the most superior assignment project according to the needing of the information war resource. The characteristics of the method is high-effective, simple, objective, wide application and improving the battle effectiveness markedly, the method can widely use for the most superior assignment of the combined operations information war resource.

Description

Resource object planning optimizing distribution of combined operation information war

Technical field the present invention relates to national defence and association area, is used for the information war resource of combined operation is carried out the goal programming optimum allocation, realizes the scientific management to the information war resource of combined operation.

Background technology worldwide, information war or information fighting are becoming the main patterns of warfare and the important means that combined operation are improved its combat capabilities, be subjected to extensive concern in campaign and tactics research field, and how the information war resource of combined operation is distributed is a difficult problem that faces in the campaign of combined operation and the tactics research always, the solution of this problem is for the whole fighting capacity that increases substantially combined operation, minimizing has crucial meaning to the demand of expensive information war resource.

In the information war resource, there are difference in essence in some resource and other traditional operating resources.At first, these information war resources have multiple fighting capacity feature usually, and the fighting capacity of various ways promptly can be provided; Secondly, these information war resources can realize distributing fast and sharing by means of network interconnection or information transfer capacity in big geographical regional extent usually, and the fighting capacity of formation can breakthrough time and the restriction in space.For example: can be by single information war resource is quantitatively adjusted, make the information war resource of distribution reach the cost optimum on the whole, compare with traditional operating resources, this optimum allocation to the information war resource can obtain to compare the higher remuneration of optimum allocation of traditional operating resources.

Expansion along with the maneuverability and the scope of combined operation, become complicated more for combined operation provide the task of the guarantee of information war resource fast, wherein outstanding contradiction is exactly how to make the bigger effect of finite information war resource performance and how to make these information war resource performances break through the advantage of space-time restriction.

On the other hand, the network-centric warfare environment has also proposed an urgent demand to the optimum allocation of information war resource, because by means of networked environments, can realize the information war resources allocation more easily, thereby make the improper information war risk that resources allocation caused also become big, so the quality of information war resource optimum allocation has more importantly influence to the fighting capacity of network-centric warfare thereupon.Therefore, the key character and the needs of network-centric warfare are not only in the optimum allocation of information war resource, and are one of network-centric warfare key issue that must solve.

In recent years, owing to be subjected to the distribution method of information war resource and to the description of information war resource and the restriction of quantization method, to the progress of the assignment problem of information war resource seldom, in fact the distribution of the information war resource of combined operation is an outstanding issue so far always.It has been generally acknowledged that fully the satisfy the demands distribution method that gets final product of information war resource not only causes the huge waste of finite information war resource, but also cause the demand of information war resource is not being met on some region of war, make the information war resource become the bottleneck that restriction fighting capacity improves, thereby cause the passive situation on the battlefield, so must seek the assignment problem that new method solves the information war resource.

The present invention relates to resource object planning optimizing distribution of combined operation information war, relate to military affairs and association area, the optimum allocation object is the information war resource of combined operation.This method at first defines the distribution of information war resource and the fighting capacity attribute of information war resource, construct then the information war resource is carried out distribution criterion, and according to index to information war fighting capacity demand, foundation is to the model of information war resource optimum allocation, and find the solution this model with The goal programming method, the final scheme that obtains according to demand the optimum allocation of information war resource, this method has efficiently, simply, objective, characteristics are widely used and obviously improve its combat capabilities etc., can be widely used in the optimum allocation of the information war resource of all combined operation, the invention further relates to the technology that realizes this method.

Summary of the invention the present invention at first defines the attribute of the fighting capacity that information war resource and each information war resource had, again according to the demand of battlefield to various different information war fighting capacity, set up the relevant Goal programming Model that is used for the optimum allocation of information war resource of demand therewith, and by finding the solution this model, the final optimum allocation that obtains the information war resource.Therefore, the conception of information war resource optimum allocation is proposed, the attribute of the fighting capacity of definition information war resource, set up with the information war resource and to the relevant information Goal programming Model of optimum allocation of the relevant information war resource of fighting capacity demand of fighting, and find the solution this model and become key character of the present invention.

The technical scheme of resource object planning optimizing distribution of combined operation information war of the present invention is:

At first, with the information war resources definition is the decision variable with some information war fighting capacity attributes, consider that simultaneously the price that different information war resources is had may be different with the fighting capacity attribute, and the target that supposition is carried out optimum allocation to the information war resource is under the constraint condition of given information war Index of Combat Effectiveness, and the total price that makes the information war resource of final assignment is minimum (can suppose that also other carries out the target of optimum allocation to the information war resource).Secondly, when considering the constraint of information war Index of Combat Effectiveness, the corresponding fighting capacity quantity of supposing all information war resources can linear superposition, and the result of stack must meet the restriction that corresponding information war Index of Combat Effectiveness is applied, claim that this logical relation that restriction constituted by stack result and information war Index of Combat Effectiveness is the constraint condition of an information war Index of Combat Effectiveness of information war resource optimum allocation objective function, fighting capacity attribute and the different of Index of Combat Effectiveness according to the information war resource can be constructed a plurality of different system restriction conditions, a plurality of different goal constraint conditions, all these constraint conditions and objective function have just constituted the Goal programming Model of information war resource optimum allocation.At last, can use the goal programming method for solving, find the solution Algebraic Equation set or model that objective function and constraint condition by the optimum allocation of information war resource constitute, can obtain optimum allocation result the information war resource.

The optimum allocation of research information war resource, usually must consider information war resource and information war resource specific implementation or and the relation of information war between equipping, because the information war equipment is the specific implementation form of information war resource, difference according to the fighting capacity attribute of information war resource itself, can regard the information war equipment as form an information war unit by the tactics of physical equipment, related personnel and employing, therefore, to the optimum allocation of information war resource, in fact be exactly optimum allocation to information war equipment itself.

The information war resource optimum allocation method of the invention is to realize with relevant constraint condition Algebraic Equation set by finding the solution the objective function of implementing optimum allocation, and the fighting capacity of information war resources allocation is required is to realize by the restriction that different fighting capacity attribute algebraic expressions is applied corresponding Index of Combat Effectiveness, so just the optimum allocation of information war resource with set up a kind of corresponding restriction relation between fighting capacity to the information war resources allocation requires, thereby the result who guarantees optimum allocation meets given fighting capacity requirement.

The resource object planning optimizing distribution of combined operation information war of the present invention's design is applicable to that the optimum allocation of the information war resource of all combined operation is key characters of the present invention.

For specific operation pattern, can be in the hope of in the information war resource that needs in this pattern, various fighting capacity resources are shared best proportion in the total information war resource of distributing, and then according to this best proportion, whole information war resource is carried out allocation optimum, therefore also can regard the optimal assignment problem of information war resource the optimization formula problem of various fighting capacity resources in the information war resource as.The case study of planning of information war resource object or multiobjective linear programming optimum allocation is as follows.

Definition x _i(i=1 ..., n) decision variable, a for information war resource i is carried out optimum allocation _IjBe the information war resource _iContain fighting capacity _j(j=1 ..., quantity m), b _jThe of the information war resource of distributing for hope _jThe Index of Combat Effectiveness that individual fighting capacity attribute reaches, c _iBe the information war resource _iPrice, then definable constitute by objective function and constraint system of equations, be used for linear programming model that n information war resource carried out optimum allocation:

Objective function MinZ is the cost minimization that makes the information war resource:

MinZ＝c ₁x ₁+…+c _nx _n

The equation of constraint group is:

a ₁₁x ₁+a ₁₂x ₂+…+a _1nx _n≥b ₁(＝，≤b ₁)

a ₂₁x ₁+a ₂₂x ₂+…+a _2nx _n≥b ₂(＝，≤b ₂)

…

a _m1x ₁+a _m2x ₂+…+a _mnx _n≥b _m(＝，≤b _m)

x ₁≥0，x ₂≥0，…，x _n≥0

Find the solution above-mentioned linear programming model by simplex algorithm, can obtain the optimum allocation result or the prescription of information war resource.Therefore, 5 condition precedents of application linear programming and multiobjective linear programming are in the optimum allocation of information war resource:

(1) severability

The information war resource (decision variable) that all are assigned with can resolve into the significant part of any size or be made up of the significant part of any size, can resolve into different information war fighting capacity and partly or by different information war fighting capacity part institutes be formed.

(2) direct proportion

For aritrary decision variable x _i, its contribution to cost is c _ix _i, be a to the contribution of j kind fighting capacity _Ijx _iIf, with x _iAmount double, also should double to cost or to the contribution of fighting capacity composition so.

(3) additive property

The total cost of the information war resource of distributing is the cost sum of each information war resource, and the information war resource of distribution is the contribution sum of a plurality of information war resources to total contribution of j constraint.

(4) consistency of axioms

In linear programming, should there be mutual repellency, co-operation together between the information war resource of Fen Peiing together.

(5) nonrandomness

All c _i, a _IjAnd b _jAll be known, deterministic, rather than at random.

Yet, although this linear programming method is simple, there is following shortcoming:

(1) has only single optimal objective, can't take into account a plurality of optimal objectives;

(2) be easy to occur not having the situation of separating;

(3) only be the optimum solution of mathematics, rather than the satisfactory solution of practical problems;

(4) solving result is single, can't screen a plurality of solving results;

(5) the fighting capacity demand of constraint condition is fixed, and can't the particular requirement of multiple factor be retrained.

Usually the primal linear programming that above-mentioned linear programming is called multiobjective linear programming, multi-objective linear programming model is to be based upon on the above-mentioned primal linear programming model based, but overcome the deficiency of primal linear programming model, can not only effectively handle the contradiction that between constraint condition and objective function, exists, but also can solve multi-objective optimization question, following rule is followed in the optimization of target:

(1) according to priority height order is optimized a plurality of targets, is prerequisite with the optimal value that does not destroy high level goal during rudimentary objective optimization;

(2) be in different target on the same priority, be optimized by the weight coefficient size.

So just can be according to the demand of information war fighting capacity and decision-maker's subjective desire, method with mathematics, all targets that need optimize by its importance degree difference, are divided into different priority, and the different target on the equal priority gives different weights.This is because when carrying out information war resource optimum allocation calculating, the importance of relevant a plurality of targets may be different, so must determine the priority and the weight of each target as the case may be, and foundation of carrying out the optimum allocation of information war resource as the goal programming system.

On above-mentioned primal linear programming model based, the mathematical model of structure multiobjective linear programming is as follows.

Be provided with n decision variable x _j(j=1,2 ..., n), the goal programming problem of L priority is arranged in the k goal constraint, a m system restriction, objective function, its general form is:

Objective function: $\min Z=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\ρ}}_l\underset{k=1}{\overset{k}{\mathrm{\Σ}}}(w_{\mathrm{lk}}^{-}{n}_k+w_{\mathrm{lk}}^{+}{p}_k)$

Goal constraint: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{c}_{\mathrm{kj}}{x}_j+n_k-p_k=g_k,$ (k＝1，2，…，k)

System restriction: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}{x}_j\≤(=,\≥)b_i,$ (i＝1，2，…，m)

Nonnegativity restrictions: x _j〉=0, (i=1,2 ..., n); n _k, p _k〉=0

In the formula:

x _j-decision variable;

a _Ij-system restriction coefficient;

c _Kj-goal constraint coefficient;

b _iThe right-hand member constant of-Di i constraint;

g _kThe expectation value an of-Di k goal constraint;

ρ _lThe priority level of-goal constraint (the preferential factor);

w _Lk ^--ρ _lN in the level target _kWeight coefficient;

w _Lk ⁺-ρ _lP in the level target _kWeight coefficient;

n _k, p _kBe deviation variables.

According to the above discussion, multiobjective linear programming comes down to mathematical model with multiobjective linear programming and is converted into common linear programming model and finds the solution.Therefore, it is as follows to find the solution the general step of multi-objective linear programming model:

The first step: set up linear programming model (comprise the hypothesis decision variable, set up equation or inequality constrain condition, set up relevant processes such as objective function) according to practical problems with m target.

Second step: multi-objective linear programming model is converted into single goal or general linear programming model:

(1), determine suitable expectation value g for k target according to practical problems _k(k=1,2 ..., k);

(2) k target introduced n _k, p _k, set up the goal constraint equation and it listed among the former constraint condition;

(3) if in the former constraint condition conflicting equation is arranged, then to they same n that introduces _kAnd p _k, more generally way is that all equation of constraint are all introduced n _kAnd p _k

(4) determine the priority level ρ of k target _lAnd weight coefficient w _Lk ^-And w _Lk ⁺

(5) set up the objective function minZ that will reach.

After finishing above-mentioned steps, just can set up linear goal planning, find the solution with simplex method then with general lexicographic order or priority.

In addition, by analysis to the dual program of above-mentioned primal linear programming, can study the economic cost of each fighting capacity binding target in the primal linear programming problem, this cost is also referred to as shadow price, optimal assignment problem for the information war resource, by finding the solution its dual problem, can carry out following quantitative test:

(1) can calculate the real economy of various information war resources in optimum allocation or optimization formula according to shadow price is worth, obviously, all information war resources that is selected into optimum allocation or optimization formula, inevitable war (city) price of its economic worth more than or equal to it, otherwise, this information war resource will fail to be elected, therefore the decision maker can judge, when which kind of level is the price of selected information war resource rise to, the proportioning of this information war resource will descend even can not continue use in relevant optimum allocation or the optimization formula, and which kind of level unelected information war resource price when dropping to, and being selected into optimum allocation again will make a profit certainly.

(2) provide the price effective range of the various information war resources of forming optimum allocation, when the price of information war resource changes in this scope, the optimum allocation result will remain unchanged, in case the price of information war resource surpasses its effective range, then need to carry out again optimum allocation, minimum to guarantee cost.

(3) valid interval of calculating Index of Combat Effectiveness, the shadow price of multiple Index of Combat Effectiveness is constant in this is interval, this moment, Index of Combat Effectiveness reduced a unit value, the information war resources costs reduction value of distributing equals the shadow price of this fighting capacity composition, and the decision maker can seek certain information war resource that the effective way that reduces cost or selection have economic benefit in view of the above.

For veneziano model by the primal linear programming model, further analyze the architectural feature of separating of above-mentioned primal linear programming model, definition is the decision variable y that describes m fighting capacity key element by objective function and constraint system of equations veneziano model that constitute, above-mentioned primal linear programming model _j(j=1 ..., linear programming model m):

Objective function MaxG reaches maximization for making the fighting capacity content's index:

MaxG＝b ₁y ₁+…+b _my _m

The equation of constraint group is:

a ₁₁y ₁+a ₂₁y ₂+…+a _m1y _m≤c ₁

a ₁₂y ₁+a ₂₂y ₂+…+a _m2y _m≤c ₂

…

a _1ny ₁+a _2ny ₂+…+a _mny _m≤c _m

y ₁≥0，y ₂≥0，…，y _m≥0

Decision variable y wherein _j(j=1,2 ..., m) for waiting to ask the Index of Combat Effectiveness b of information war resource _j(j=1,2 ..., shadow price m) or opportunity cost.

Find the solution above-mentioned dual linear programming model by simplex algorithm, can finish antithesis analysis above-mentioned primal linear programming.

Under network center's environment, the information war resource can realize all or part of quick distribution, and this being distributed in fast is quick distribution to the fighting capacity attribute of information war resource in essence, and the common fighting capacity that can distribute fast has target reconnaissance, targeted surveillance, goal-based assessment and to processing of target information etc.Since each information war resource all may and a certain concrete information war equipment or troops between have corresponding relation, and may have fighting capacity partly or entirely, also be quick optimum allocation in itself to the quick optimum allocation of information war resource to relevant information war equipment or troops.

Must be pointed out: in the process of actual information war resource optimum allocation, finally to implement to the optimum allocation of information war resource the branch of information war equipment or troops is mixed, therefore must consider that information war equipment or troops itself measure with integer, and the solving result of above-mentioned multiobjective linear programming is equipped by information war or the quantity of troops is non-integer, so just might make this non-integer allocation result in concrete realization by integer, thereby have influence on the correctness of multiobjective linear programming optimum solution.But on the other hand, can realize under network center's environment that the information war that distributes is fast equipped or the value of the fighting capacity attribute of troops own can be in the certain limit adjustment, therefore the non-integer allocation result in fact also can realize, so just can guarantee the correctness of optimum allocation result in specific implementation.

Embodiment

Embodiment 1

At first be planned to campaign X assignment information war resource with common linearity.

Supposition now must be carried out optimum allocation to the information war resource of combined operation in a typical campaign planning, consider X altogether ₁, X ₂, X ₃, X ₄, X ₅And X ₆Deng 6 kinds of information war resources, the information war resource requirement that is distributed satisfies the fighting capacity requirement of X campaign, and cost is minimum.

The fighting capacity of each information war resource can be described with 13 fighting capacity attributes, wherein y ₁And y ₂Relevant with battlefield target reconnaissance ability or fighting capacity, y ₃And y ₄Relevant with battlefield targeted surveillance fighting capacity, y ₅And y ₆Relevant with the battlefield to target strike effect assessment (BDA) fighting capacity, y ₇And y ₈Relevant to target information processing fighting capacity with the battlefield, all the other attack relevant with information transmission fighting capacity with battle field information.

The information war resource is carried out in the process of optimum allocation in the utilization linear programming, have two subject matters.At first, linear programming mainly is to consider bestly economically during to the information war resources allocation, and cost as unique target that is optimized, is not considered other factors.Secondly, the Index of Combat Effectiveness relevant with linear programming constraint condition must obtain definitely satisfied, and in fact to the demand of any fighting capacity all be have necessarily flexible, therefore, in most of the cases, in order to satisfy the requirement of a certain Index of Combat Effectiveness, just might cause the waste of other multiple fighting capacity, thereby reduce the utilization factor of information war resource.Yet these problems of linear programming can solve by adopting multiple objective programming.

For the campaign X on first region of war, can be campaign X assignment information war resource with linear programming method, table 1 is the linear programming model of implementation information war resource optimum allocation.In table l, the connotation of constraint condition (14) is fighting capacity Y ₁₃In to have 20% amount at least be from information war resource X ₁And X ₂, retrain (16) and then represent information war resource X ₃At fighting capacity Y ₁₄In shared component must not surpass 20%.

The linear programming model of table 1 information war resource optimum allocation

		X 1	X 2	X 3	X 4	X 5	X 6	Transfering variable
										1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17	Price (ten thousand yuan) Y 1 Y 2 Y 3 Y 4 Y 5 Y 6 Y 7 Y 8 Y 9 Y 10Contact constraint Y 11 Y 12 Y 13 X 4 X 3 X 1	48.2 10.3 108.0 19.0 3.9 3.3 1.6 3.8 5.7 0.09 1.O 1.0 0.56 0.56 -0.8 0 -0.2 1.0	26.8 6.5 32.0 8.0 2.7 0.9 0.7 1.1 3.2 0.04 1.0 1.0 0.35 0.35 -0.8 0 -0.2 0	69.8 10.3 138.6 59.4 1.7 3.7 1.4 0.9 10.0 0.2 1.0 1.0 0.56 0.56 0.2 0 0.8 0	92.6 12.8 97.2 10.8 3.6 3.2 1.2 2.6 3.8 0.04 1.0 1.0 0.70 0.70 O.2 1.0 -0.2 0	105.6 13.0 105.3 11.7 0.5 4.0 1.3 0.2 4.8 0.04 1.0 1.0 0.71 0.71 0.2 0 -0.2 0	162.5 12.8 107.2 52.8 11.4 8.5 3.5 5.4 19.0 1.50 1.0 1.0 0.70 0.70 0.2 0 -0.2 0	0.0 0.0 0.0 0.0 0.0 0.O 0.0 0.0 0.0 0.0 0.0 -1.0 -0.637 -0.642 0.0 0.0 0.0 0.0	≥213.3 ≥1663.3 ≥620.5 ≥73.6 ≥67.8 ≥24.0 ≥26.9 ≥180.0 ≥2.0 ≤19.0 ＝0.0 ≥O.0 ≤0.0 ≤0.0 ≤2.0 ≤0.0 ≤6.8

The objective function of the information war resource optimum allocation that structure is relevant is:

minZ＝0.0482x ₁+0.0268x ₂+0.0698x ₃+0.0924x ₄+0.1056x ₅+0.1625x ₆

Wherein: the optimum allocation amount of various information war resources to be asked or select ratio x for use _i(i=1,2 ..., 6) preceding coefficient is the price of information war resource (ten million yuan/unit resource).

Transfering variable in the table 1 by contact constraint condition, is used for each information war resource is limited in the shared share of the information war total resources of optimum allocation, simultaneously also to fighting capacity Y ₁₁And Y ₁₂Span limit, even Y ₁₁And Y ₁₂Value be controlled in the reasonable range.

Table 2 and table 3 are the optimum allocation result or the prescription of the information war resource obtained by the simplex algorithm of finding the solution linear programming model, and least cost is 1.782 (ten million yuan), and the optimum allocation result satisfies the requirement of Index of Combat Effectiveness.

The result of calculation of table 2 linear programming method

	X 1	X 2	X 3	X 4	X 5	X 6
							Consumption	4.981	0.00	3.436	2.00	2.778	5.069
Total price	Min Z=1.782 (ten million yuan)

Table 3 information war resource linear programming optimum allocation result

The fighting capacity component	Index of Combat Effectiveness (requirement)	The optimum allocation result
			Y 1 Y 2 Y 3 Y 4 Y 5 Y 6 Y 7 Y 8 Y 9 Y 10	213.3 1663.3 620.5 73.6 67.8 24.0 26.9 180.0 2.0 19.0	213.3 2044.6 620.5 91.6 89.8 36.5 55.1 180.0 8.9 18.30

Embodiment 2

With the weighting goal programming is campaign X assignment information war resource.

By table 3, can the fighting capacity component of information war resource allocation result be compared with the Index of Combat Effectiveness that will reach.As can be seen from Table 3, fighting capacity require constraint very tight Y only arranged ₁, Y ₃And Y ₈But several fighting capacity compositions, particularly Y are arranged ₆, Y ₇And Y ₉, having surpassed requirement, this is that information war resource optimum allocation institute is unallowed.Although can be by every kind of fighting capacity is determined its bound, and set up the dependent linearity plan model and find the solution, under situation mostly, because too little between the bound confining region, may cause linear programming not have and separate.In order to address this problem, can be when setting up optimal allocation model, the minimizing of the fighting capacity redundance in the minimum cost prescription as the target that will reach.

Except that cost and information war fighting capacity were distributed imbalance, another major issue was relevant to the information war resource the distribution of computer network to enemy's Computer Network Attack(CNA) ability size in the information war resources allocation.When too big, will consider the adverse effect that to bring to the Computer Network Attack(CNA) ability when this information war resource.Therefore, reduce the information war resource of distributing the Computer Network Attack(CNA) ability be can be used as a target.Consider these factors, determine that three different targets of the linear programming model in the table 1 are:

(1) makes the cost minimum of the information war resource of distribution;

(2) make the information war fighting capacity Y of distribution ₆, Y ₇And Y ₉Unnecessary amount be minimum;

(3) make the information war resource of distribution be minimum to the Computer Network Attack(CNA) ability.

It is as follows that application weighting goal programming solves information war resource optimal assignment problem.

The weighting goal programming is by different targets is weighted, promptly in a synthetic objective function, consider all targets simultaneously, make target wish that deviation is for minimum between the level that reaches and the actual result, can inequality be converted into equation realize the weighting goal programming by in the inequality relevant, increasing the positive and negative deviation variable with constraint condition.By introducing departure, allowing each target can reach can not reach yet, and according to the relative importance of each target, in objective function, gives different weights to these deviations.

Now realize above-mentioned three elementary objects by 5 different objectives.

Target G1:

Relevant with the information war resource should be greater than 40 to the Computer Network Attack(CNA) ability.From table 4, can obtain various information war resources relevant to the Computer Network Attack(CNA) ability.

Table 4 information war resource is to the Computer Network Attack(CNA) ability

The information war resource	X 1	X 2	X 3	X 4	X 5	X 6
							To the Computer Network Attack(CNA) ability	3.074	1.219	3.876	9.259	1.200	1.137

Target G1 can describe with following formula:

g ₁＝3.704x ₁+1.219x ₂+3.876x ₃+9.259x ₄+1.200x ₅+1.137x ₆+n ₁-p ₁＝40

The deviation n here ₁Expression does not reach the departure of target G1, and P ₁Then expression surpasses the departure of G1 target.Owing to wish that the information war resource should be greater than 40, so should make deviation P to the Computer Network Attack(CNA) ability ₁Reach minimum.

Target G2:

In the information war resource of distributing, fighting capacity Y ₇Content should not surpass 100% of demand.From the constraint (7) of table 1, can obtain uneven target and be:

g ₂＝3.8x ₁+1.1x ₂+0.9x ₃+2.6x ₄+0.2x ₅+5.4x ₆-26.9

Transfer the percentage of above-mentioned equation to absolute number, then have:

$\frac{({3.8x}_1+{1.1x}_2+{0.9x}_3+{2.6x}_4+{0.2x}_5+{5.4x}_6-26.9)\×100}{26.9}$

Therefore the expression formula of G2 is:

g ₂＝14.13x ₁+4.09x ₂+3.35x ₃+9.67x ₄+0.74x ₅+20.07x ₆+n ₂-p ₂＝200

In order to reach the level of this target, must make P2 reach minimum.

Target G3 and G4:

Adopt and the similar method of G2, can from table 1, obtain Y ₈, Y ₉Target.Y ₈And Y ₉Content also should not surpass 100% of demand.Two targets are given as follows:

g ₃＝3.17x ₁+1.78x ₂+5.55x ₃+2.11x ₄+2.67x ₅+10.55x ₆+n ₃-p ₃＝200

g ₄＝4.5x ₁+2x ₂+10x ₃+2x ₄+2x ₅+75x ₆+n ₄-p ₄＝200

In order to reach target G3 and G4, P ₃And P ₄Be necessary for minimum value.

Target G5:

The minimum cost 1.782 that to try to achieve by linear programming is as the indicator of costs, and with reference to the price of multiple information war resource in the table 1, target G5 can be expressed as:

g ₅＝0.0482x ₁+0.0268x ₂+0.0698x ₃+0.0924x ₄+0.1056x ₅+0.1625x ₆+n ₅-p ₅＝1.782

In order to reach G5, must make P ₅Reach minimum.

Because when adopting absolute deviation, the variable of objective function is subjected to the influence of different linear modules and becomes meaningless, so the variable of objective function should adopt the percent deviation of divergence indicator.Therefore, in the weighting Goal programming Model, with the each several part standardization of objective function, consider the situation of a priority here, and use W _kReplace w _Lk ⁺, can obtain following formula:

$w_1\frac{p_1}{40}\·\frac{100}{1}+w_2\frac{p_2}{200}\·\frac{100}{1}+w_3\frac{p_3}{200}\·\frac{100}{1}+w_4\frac{p_4}{200}\·\frac{100}{1}+w_5\frac{p_5}{1.782}\·\frac{100}{1}$

Or: 2.5w ₁p ₁+ 0.50w ₂p ₂+ 0.5w ₃p ₃+ 0.5w ₄P ₄+ 56.12w ₅p ₅

The W here ₁..., W ₅Represent the weight coefficient relevant, in table 5, provided 11 groups of typical weight coefficients with the significance level of a plurality of targets.

The weight coefficient of table 5 weighting goal programming

	W 1	W 2	W 3	W 4	W 5
						1 2 3 4 5 6 7	1 1 2 1 1 3 1	1 2 1 1 3 1 1	1 2 1 1 3 1 1	1 2 1 1 3 1 1	1 1 1 2 1 1 3

8 9 10 11

1 1 2 1

1 2 1 1

1 2 1 1

1 2 1 1

4 4 4 5

Through above-mentioned standardization conversion, the weighting multiple objective programming is exactly common linear programming problem on mathematics, can find the solution by simplex algorithm.By giving W _kParameter is provided with different values, can obtain different separating, and has provided separating of 11 groups of typical weight coefficient correspondences in table 6.

The weighting multiple objective programming that table 6 is corresponding with 11 groups of weight coefficients is separated

	X 1	X 2	X 3	X 4	X 5	X 6	n 1	P1	n 2	P2	n 3	P3	n 4	P4	n 5	P5
																	1 2 3 4 5 6 7 8 9 10 11	3.511 4.508 2.923 3.511 5.144 2.923 4.911 4.911 5.144 4.275 4.911	0.676 0.000 0.917 0.676 0.000 0.917 0.000 0.000 0.000 0.263 0.000	3.800 3.800 3.800 3.800 3.800 3.800 3.652 3.652 3.800 3.652 3.652	0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000	6.298 6.116 6.518 6.298 5.520 6.518 4.843 4.843 5.520 5.147 4.843	4.716 4.576 4.842 4.716 4.536 4.842 4.855 4.855 4.536 4.924 4.855	0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000	1.476 3.969 0.000 1.476 5.564 0.000 3.678 3.678 5.564 2.086 3.678	35.596 27.198 40.222 35.596 19.461 40.222 17.354 17.354 19.461 23.643 17.354	0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000	100.013 100.011 99.528 100.013 100.011 99.528 100.015 100.015 100.011 100.016 100.015	0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000	0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000	221.414 213.736 229.156 221.414 212.383 229.156 232.408 232.408 212.383 235.911 232.408	0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000	0.102 0.090 0.124 0.102 0.051 0.124 0.010 0.010 0.051 0.030 0.010

For example, establish W ₁=W ₂=W ₃=W ₄=W ₅=1, then can obtain following optimum solution by simplex algorithm:

X ₁＝3.511、X ₂＝0.675、X ₃＝3.8、X ₄＝0、X ₅＝6.298、X ₆＝4.716。

The optimal value of deviation variables is:

n ₁＝0、n ₂＝35.59％、n ₃＝100％、n ₄＝0、n ₅＝0、p ₁＝1.477、p ₂＝0、p ₃＝0、p ₄＝221.41％、p ₅＝0.102。

By P ₂=P ₃=0 as can be seen, realized target G2 and target G3 in this separates fully.P ₁Value be the index 1.477 that 1.477 expression target G1 have surpassed it.Equally, P ₄The supply of=221.41% expression Y9 be decide 321.41% of demand.At last, P ₅The expense of=0.102 this optimum allocation of expression has more 0.102 than the index 1.782 that sets.

The sensitivity analysis that the weighting goal programming is separated can provide Useful Information for working out information war resource optimal distributing scheme, has provided 11 groups of weight coefficients in table 5, and provide corresponding sensitivity analysis result in table 7.

The sensitivity analysis that the weighting multiple objective programming of table 7 pair 11 groups of weight coefficient correspondences is separated

	X 1	X 2	X 3	X 4	X 5	X 6	G 1/P1		G 2/P2		G 3/P3		G 4/P4		G 5/P5
																	1 2 3	3.511 4.506 2.923	0.675 0.000 0.917	3.800 3.800 3.800	0.000 0.000 0.000	6.298 6.118 6.519	4.716 4.576 4.842	41.476 43.969 40.000	1.476 3.969 0.000	64.404 72.802 59.779	0.000 0.000 0.000	0.000 0.000 0.472	0.000 0.000 0.000	321.414 313.736 329.156	221.414 213.736 229.156	1.884 1.872 1.906	0.102 0.090 0.124

4 5 6 7 8 9 10 11

3.511 5.144 2.923 4.911 4.911 5.144 4.275 4.911

0.675 0.000 0.917 0.000 0.000 0.000 0.263 0.000

3.800 3.800 3.800 3.652 3.652 3.800 3.652 3.652

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

6.298 5.520 6.519 4.843 4.843 5.520 5.147 4.843

4.716 4.536 4.842 4.855 4.855 4.536 4.924 4.855

41.476 45.564 40.000 43.678 43.678 45.564 42.086 43.678

1.476 5.564 0.000 3.678 3.678 5.564 2.086 3.678

64.404 80.539 59.779 82.646 82.646 80.539 76.357 82.646

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.472 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

321.414 312.383 329.156 332.408 332.408 312.383 335.911 332.408

221.414 212.383 229.156 232.408 232.408 212.383 235.911 232.408

1.004 1.833 1.906 1.792 1.792 1.833 1.812 1.792

0.102 0.051 0.124 0.010 0.010 0.051 0.030 0.010

By analysis, can find out only separating to the two.For example, conciliate 2 as can be seen if the decision maker relatively separates 1, though the latter Duos 2.493 than the former, expense has reduced by 0.012.Y ₈, Y ₉Unnecessary amount descended 7.68%, so the latter is more favourable.Therefore, a large amount of information that utilization provides in different schemes, make the decision maker can select to satisfy the optimal distributing scheme of its needs, the influence that promptly can utilize the sensitivity analysis result and study to the different weight coefficients of different Target Setting the relation that between each target, exists that whole information war resources allocation is constituted, thus more decision-making foundation provided for the decision maker.

Claims (8)

1, the present invention relates to the information war resource object planning optimizing distribution of combined operation, relate to military affairs and association area, the optimum allocation object is the information war resource of combined operation, this method at first defines the distribution of information war resource and the fighting capacity attribute of information war resource, construct then the information war resource is carried out distribution criterion, and according to index to information war fighting capacity demand, foundation is to the model of information war resource optimum allocation, and find the solution this model with The goal programming method, the final optimal distributing scheme that obtains according to demand the information war resource, this method has efficiently, simply, objective, characteristics are widely used and obviously improve its combat capabilities etc., can be widely used in the optimum allocation of the information war resource of all combined operation, the invention further relates to the technology that realizes this method.

2, the information war resource object planning optimizing distribution of combined operation according to claim 1, it is characterized in that information war resource that described optimum allocation object is combined operation is meant the information war resource of the combined operation object as optimum allocation, actual demand according to region of war or operation, optimum allocation partial information war resource is given region of war or operation from this object, what promptly solve is according to actual needs, optimum allocation partial information war problem of resource from overall information war resource.

3, the information war resource object planning optimizing distribution of combined operation according to claim 1, when it is characterized in that information war resource that described optimum allocation object is combined operation is meant the optimum allocation of research information war resource, usually must consider information war resource and information war resource specific implementation or and the relation of information war between equipping, because the information war equipment is the specific implementation form of information war resource, difference according to the fighting capacity attribute of information war resource itself, the information war equipment can be regarded as by physical equipment, the information war unit that the tactics of related personnel and employing are formed, therefore, to the optimum allocation of information war resource, in fact be exactly optimum allocation to information war equipment itself.

4, the information war resource object planning optimizing distribution of combined operation according to claim 1, the fighting capacity attribute that it is characterized in that described distribution that at first defines the information war resource and information war resource is meant in the part of resource that overall information is fought distributes to the region of war, when operation or other object, think that the information war resource has multiple fighting capacity or has multiple fighting capacity attribute, and the percentage that is used in different information war fighting capacity contained in the unit information war resource comes the information war fighting capacity attribute of quantitative description information war resource, be that the information war resource is a kind of resource with multiple information war fighting capacity or fighting capacity attribute, this also is the important foundation that the information war resource can be carried out optimum allocation.

5, the information war resource object planning optimizing distribution of combined operation according to claim 1, it is characterized in that described the structure then carry out distribution criterion to the information war resource and be meant that distribution portion information war resource is carried out according to some predetermined criteria or rule from overall information war resource, the distribution of satisfying these criterions or rule to greatest extent is also referred to as optimum allocation, and the functional form of these criterions or rule is called the objective function of implementing optimum allocation, and can set up different criterions or rule according to actual needs on their own, for example: in order to guarantee most economical use to overall information war resource, can set up the minimum cost objective function relevant with " most economical using priciple " and implement optimum allocation, promptly distribution portion information war resource is finished as target by predetermined criteria or rule from overall information war resource.

6, the information war resource object planning optimizing distribution of combined operation according to claim 1, it is characterized in that described and according to index to information war fighting capacity demand, foundation is meant concerning a side of information war resource requirement the model of information war resource optimum allocation, can be according to the actual demand of its region of war, place or operation, proposition (can be passed through Combat Simulation usually to the specific requirement of information war fighting capacity, experimental formula or other any way are determined the real needs to information war fighting capacity), these demands are then in the optimum allocation of information war resource, be used as the constraint condition that optimum allocation must be satisfied, and then on the basis of the constraint condition of the objective function of optimum allocation and optimum allocation, the model of structure implementation information war resource optimum allocation, promptly having the objective function of optimum allocation and the constraint condition of optimum allocation is the key character of information war resource optimal allocation model.

7, the information war resource object planning optimizing distribution of combined operation according to claim 1, it is characterized in that described and find the solution this model with The goal programming method, the final optimal distributing scheme that obtains according to demand the information war resource is meant and following the information war resource is carried out the goal programming equation of optimum allocation and by finding the solution the optimal distributing scheme of the information war resource that this equation obtains, but following mathematical formulae, derivation, result of calculation and application process are applicable to the optimum allocation to the information war resource of all combined operation

For specific operation pattern; Can be in the hope of in the information war resource that needs in this pattern; Various fighting capacity resources are shared best proportion in total information war resource; And then according to this best proportion; Whole information war resource is carried out allocation optimum; Therefore also can be with the optimal assignment problem of information war resource; Regard the optimization formula problem of various fighting capacity resources in the information war resource as; The planning of information war resource object or multiobjective linear programming optimum allocation method can further describe as follows

Definition x _i(i=1 ..., n) decision variable, a for information war resource i is carried out optimum allocation _IjBe the information war resource _iContain fighting capacity _j(j=1 ..., quantity m), b _jThe of the information war resource of distributing for hope _jThe Index of Combat Effectiveness that individual fighting capacity attribute reaches, c _iBe the information war resource _iPrice, then definable constitutes, is used for linear programming model that n information war resource carried out optimum allocation by objective function and constraint system of equations:

Objective function MinZ is the cost minimization that makes the information war resource:

MinZ＝c ₁x ₁+…+c _nx _n

The equation of constraint group is:

a ₁₁x ₁+a ₁₂x ₂+…+a _1nx _n≥b ₁(＝，≤b ₁)

a ₂₁x ₁+a ₂₂x ₂+…+a _2nx _n≥b ₂(＝，≤b ₂)

…

a _m1x ₁+a _m2x ₂+…+a _mnx _n≥b _m(＝，≤b _m)

x ₁≥0，x ₂≥0，…，x _n≥0

Find the solution above-mentioned linear programming model by simplex algorithm, can obtain the optimum allocation result or the prescription of information war resource, therefore, 5 condition precedents using linear programming and multiobjective linear programming in the optimum allocation of information war resource are:

(1) severability

The information war resource (decision variable) that all are assigned with can resolve into the significant part of any size or be made up of the significant part of any size, can resolve into different information war fighting capacity partly or by different information war fighting capacity part institutes is formed

(2) direct proportion

For aritrary decision variable x _i, its contribution to cost is c _ix _i, be a to the contribution of j kind fighting capacity _Ijx _iIf, with x _iAmount double, also should double to cost or to the contribution of fighting capacity composition so,

(3) additive property

The total cost of the information war resource of distributing is the cost sum of each information war resource, and the information war resource of distribution is the contribution sum of a plurality of information war resources to total contribution of j constraint,

(4) consistency of axioms

In linear programming, should there be mutual repellency between the information war resource of Fen Peiing together, co-operation together,

(5) nonrandomness

All c _i, a _IjAnd b _jAll be known, deterministic, rather than at random,

Yet, although this linear programming method is simple, there is following shortcoming:

(1) has only single optimal objective, can't take into account a plurality of optimal objectives;

(2) be easy to occur not having the situation of separating;

(3) only be the optimum solution of mathematics, rather than the satisfactory solution of practical problems;

(4) solving result is single, can't screen a plurality of solving results;

(5) the fighting capacity demand of constraint condition is fixed, can't the particular requirement of multiple factor be retrained,

Usually the primal linear programming that above-mentioned linear programming is called multiobjective linear programming, multi-objective linear programming model is to be based upon on the above-mentioned primal linear programming model based, but overcome the deficiency of primal linear programming model, can not only effectively handle the contradiction that exists each other at constraint condition and objective function, but also can solve multi-objective optimization question, following rule is followed in the optimization of target:

(1) according to priority height order is optimized a plurality of targets, is prerequisite with the optimal value that does not destroy high level goal during rudimentary objective optimization;

(2) be in different target on the same priority, be optimized by the weight coefficient size,

So just can be according to the demand of information war fighting capacity and decision-maker's subjective desire; Method with mathematics; All targets that need to optimize are different by its importance degree; Be divided into different priority; Different target on the equal priority gives different weights; This is because when carrying out information war resource optimum allocation calculating; The importance of relevant a plurality of targets may be different; So must determine as the case may be priority and the weight of each target; And the foundation of carrying out the optimum allocation of information war resource as the goal programming system

On above-mentioned primal linear programming model based, the mathematical model of structure multiobjective linear programming is as follows,

Be provided with n decision variable x _j(j=1,2 ..., n), the goal programming problem of L priority is arranged in the k goal constraint, a m system restriction, objective function, its general form is:

Objective function: $\min Z=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\ρ}}_l\underset{k=1}{\overset{k}{\mathrm{\Σ}}}(w_{\mathrm{lk}}^{-}{n}_k+w_{\mathrm{lk}}^{+}{p}_k)$

Goal constraint: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{c}_{\mathrm{kj}}{x}_j+n_k-p_k=g_k,$ (k＝1，2，…，k)

System restriction: $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}{x}_j\≤(=,\≥)b_i,$ (i＝1，2，…，m)

Nonnegativity restrictions: x _j〉=0, (i=1,2 ..., n); n _k, p _k〉=0

In the formula:

x _j-decision variable;

a _Ij-system restriction coefficient;

c _Kj-goal constraint coefficient;

b _iThe right-hand member constant of-Di i constraint;

g _kThe expectation value an of-Di k goal constraint;

ρ _lThe priority level of-goal constraint (the preferential factor);

w _Lk ^--ρ _lN in the level target _kWeight coefficient;

w _Lk ⁺-ρ _lP in the level target _kWeight coefficient;

n _k, p _kBe deviation variables,

According to the above discussion, multiobjective linear programming comes down to mathematical model with multiobjective linear programming and is converted into ordinary lines part plan model and finds the solution, and therefore, the general step of finding the solution multi-objective linear programming model is as follows:

The first step: set up linear programming model (comprise the hypothesis decision variable, set up equation or inequality constrain condition, set up relevant processes such as objective function) according to practical problems with m target,

Second step: multi-objective linear programming model is converted into single goal or general linear programming model:

(1), determine suitable expectation value g for k target according to practical problems _k(k=1,2 ..., k);

(2) k target introduced n _k, p _k, set up the goal constraint equation and it listed among the former constraint condition;

(3) if in the former constraint condition conflicting equation is arranged, then to they same n that introduces _kAnd p _k, more generally way is that all equation of constraint are all introduced n _kAnd p _k

(4) determine the priority level ρ of k target _lAnd weight coefficient w _Lk ^-And w _Lk ⁺

(5) set up the objective function minZ that will reach,

After finishing above-mentioned steps, just can set up linear goal planning, find the solution with simplex method then with general lexicographic order or priority.

8, the information war resource object planning optimizing distribution of combined operation according to claim 1, it is characterized in that described and find the solution this model with The goal programming method, the final optimal distributing scheme that obtains according to demand the information war resource is meant that the former veneziano model that carries out the Goal programming Model of information war resource optimum allocation can be used to analyze the satisfaction degree of Index of Combat Effectiveness of primal linear programming model to the influence of the satisfaction degree of objective function, promptly be used for determining of the influence of the satisfaction degree of Index of Combat Effectiveness to the satisfaction degree of objective function, following mathematical formulae, derivation, result of calculation and application process are applicable to the antithesis analysis to the optimum allocation of the information war resource of all combined operation

By analysis to the dual program of above-mentioned primal linear programming, can study the economic cost of each fighting capacity binding target in the primal linear programming problem, this cost is also referred to as shadow price, optimal assignment problem for the information war resource, by finding the solution its dual problem, can carry out following quantitative test:

(1) can calculate the real economy of various information war resources in optimum allocation or optimization formula according to shadow price is worth, obviously, all information war resources that is selected into optimum allocation or optimization formula, inevitable war (city) price of its economic worth more than or equal to it, otherwise, this information war resource will fail to be elected, therefore the decision maker can judge, when which kind of level is the price of selected information war resource rise to, the proportioning of this information war resource will descend even can not continue use in relevant optimum allocation or the optimization formula, and which kind of level unelected information war resource price when dropping to, and will be selected into optimum allocation will make a profit certainly

(2) provide the price effective range of the various information war resources of forming optimum allocation, when the price of information war resource changes in this scope, the optimum allocation result will remain unchanged, in case the price of information war resource surpasses its effective range, then need to carry out again optimum allocation, minimum to guarantee cost

(3) valid interval of calculating Index of Combat Effectiveness, the shadow price of multiple Index of Combat Effectiveness is constant in this is interval, this moment, Index of Combat Effectiveness reduced a unit value, the information war resources costs reduction value of distributing equals the shadow price of this fighting capacity composition, the decision maker can seek certain information war resource that the effective way that reduces cost or selection have economic benefit in view of the above

For veneziano model by the primal linear programming model, further analyze the architectural feature of separating of above-mentioned primal linear programming model, definition is the decision variable y that describes m fighting capacity key element by objective function and constraint system of equations veneziano model that constitute, above-mentioned primal linear programming model _j(j=1 ..., linear programming model m):

Objective function MaxG reaches maximization for making the fighting capacity content's index:

MaxG＝b ₁y ₁+…+b _my _m

The equation of constraint group is:

a ₁₁y ₁+a ₂₁y ₂+…+a _m1y _m≤c ₁

a ₁₂y ₁+a ₂₂y ₂+…+a _m2y _m≤c ₂

…

a _1ny ₁+a _2ny ₂+…+a _mny _m≤c _m

y ₁≥0，y ₂≥0，…，y _m≥0

Decision variable y wherein _j(j=1,2 ..., m) for waiting to ask the Index of Combat Effectiveness b of information war resource _j(j=1,2 ..., shadow price m) or opportunity cost,

Find the solution above-mentioned dual linear programming model by simplex algorithm, can finish antithesis analysis above-mentioned primal linear programming.